Sessão Temática 5

Adaptativity of the least square estimator

Leandro P. R. Pimentel* (Delft University of Technology, Netherlands, The Netherlands)

In the white noise model the increment of the observable is the sum of two components: a deterministic drift and a white noise. The deterministic drift is assumed to belong to some class of functions (e.g. linear, convex or monotone). We focus on the following inverse problem: given the history of the observable, how to estimate the drift? It is a long standing fact that the least square estimator fits as a good candidate for that. In this talk we present a simple technique that shows that this estimator is fully adaptative, in the sense that the attained covergence rate is given by a functional relation using the underlying function and the error operator (and not by some smoothness parameter).

*This is a joint work with E. Cator from Delft Univ. of Technology (Netherlands)